1. Consider a Steel producer with the cost function given by

Cost = 30 + 6Q²

a. I f market price of steel is $102 per unit, find the firms optimal quantity and maximum profit level.

b. Suppose that each unit of steel production produces 6 units of pollution. Suppose further that scientists have conducted a study on similar steel factory pollution and determined that pollution is related to days missed from work according to the following equation

               Sick Days = 0.6(Q)+10

Assuming the daily wage is $12 what is the marginal social cost of the pollution?

c.  What is the total social cost of pollution when the firm considers only its private costs.

d.  What is the optimal per unit tax on pollution for this steel factory. Why?  Show using a well labeled graph that your tax will achieve a socially optimal level of output.

e. Suppose the firm has property rights over the surrounding air, and that there are 15 people in the affected area around the factory. Will these people be able to coordinate and pay the firm to stop producing? If so, how much will they pay the firm and what will the final level of output be?

f. Do you prefer the solution in e or the solution in d? Why?

2. Suppose the Steel producer from problem 1 is a monopoly.  How might this affect the optimal per unit tax? Explain in words and using a graph.

3. Consider the market for two goods, Bread and Pants. Assume that there are sufficient resources in the economy to product B loaves of bread and P pants. Suppose that the price of bread is p_b and the price of pants is p_p. 

a. Describe production functions for Bread and Pants. Where L is the total amount of labor available and K is the total amount of capital available in the economy/

b. Use an edgeworth box to identify the locus of efficient combinations of production of bread and pants.

c. Plot these efficient bundles on a graph with Bread on the X-axis and Pants on the Y-axis.  Describe this graph.

d. Using another edgeworth box describe the consumers potential optimal choice of consumption of Bread and Pants.

e. Describe the conditions for a socially optimum level of consumption and production of Bread and Pants. Use both words and a graph.

4. Assume you are speaking to a 5 year old. Explain why a market economy will lead to an efficient solution.

a. The 5 year old rebuts your explanation with the question, "why are drugs illegal then? shouldnt a well functioning market for narcotics yield and efficient level of drug consumption and production?" What is your response?